A granular material, or granular composite, is an accumulation of constituent particles, where each constituent has a pre-determined geometry (size and shape) that remains approximately fixed when the constituents are placed in close proximity and pressed against one another, for example, by gravity. In a granular composite, the constituents may also be suspended in a solvent or liquid or held approximately or exactly fixed in place by a “paste” or “glue”. Granular composites are ubiquitous throughout industry, research labs, and the natural world. Common examples of granular composites in the natural world include dirt, sand, and gravel; common examples of man-made granular composites include concrete, bird shot, sugar, baby powder, solid propellants, cermets, ceramics, inks, and colloids.
The physical characteristics of a granular composite depend intimately on the detailed multi-bodied structure that is formed through the physical interaction of its constituent particles, and on the physical characteristics of the materials that comprise the constituents. These characteristics include but are not limited to: porosity (fraction of void space not filled by constituent particles), viscosity, mechanical strength, ductility, tensile strength, elastic modulus, bulk modulus, shear modulus, thermal conductivity, electrical conductivity, and thermal expansion coefficient. For example, a composite consisting of a given type of material with a higher-porosity structure will generally be less strong, thermally conductive, and electrically conductive than a composite consisting of the same type of material but with a lower-porosity structure. Or, a composite consisting of constituents that tend to be very rough (high coefficients of friction) and aspherical in shape will, when randomly mixed, generally form a less-dense (higher porosity) structure than a composite consisting of constituents of the same material but where the constituents are relatively less rough and apsherical.
The study of granular composites and their applications has generally focused on measuring both the physical characteristics of a given composite and the geometric size, shape, and other physical characteristics of its constituent particles. For example, in the concrete industry, where crushed rock and sand are mixed with wet cement (the “paste”) in certain proportions to form concrete, a “passing curve” is often used to approximately represent the size distribution of constituent particles in the mixture. This “passing curve” is generated by passing the dry mixture of sand and crushed rock (also called the aggregate) through a succession of finer and finer sieves, then plotting the volume (or mass) fraction of aggregate that has passed through each sieve. It is known that changing the size distribution of particles, for example, by reducing the amount of smaller-sized aggregate (the sand, in this case), can change the physical characteristics of the wet concrete, for example, wet concrete viscosity, and also of the dried and set concrete, for example, concrete elastic moduli and durability. In this way, some researchers have sought to improve concrete properties by changing the mixing ratios of aggregates. F. de Larrard, Concrete optimization with regard to packing density and rheology, 3rd RILEM international symposium on rheology of cement suspensions such as fresh concrete, France (2009). J. M. Shilstone, Jr., and J. M. Schilstone, Sr., Performance based concrete mixtures and specifications for today, Concrete International, 80-83, February (2002). F. de Larrard, Concrete mixture proportioning, Routledge, N.Y. (1999). J. M. Schilstone, Concrete mixture optimization, Concrete International, 33-40, June (1990).
However, the broad problem of designing granular composites based on constituent geometry and characteristics has not been generally tractable due to its immense complexity. The characteristics of a composite depend not only on the detailed geometry and physical characteristics of each and every component constituent, but also upon the position, orientation, and arrangement of every particle in the composite. For example, a composite structure that is obtained by shaking constituents in a closed container and then pouring into another container will have a different porosity than a structure generated from the exact same constituents by vibrating at high frequency in a container. This difference can be quite large, for example, as much as 50% less porosity for the vibrated preparation, and the inherent differences between the different porosity structures will have a pronounced effect on the physical characteristics of the composite.
For example, in concrete, the mechanical strength of a concrete has been shown to depend exponentially on the porosity of the aggregate mixture, with mixtures exhibiting less porosity being exponentially stronger. However, the viscosity, inversely related to ease of flow, also depends exponentially on the porosity, with mixtures exhibiting less porosity flowing less well (having higher viscosity). A concrete must flow to some extent in order to be poured at a job site, and as such more porosity in the aggregate mixture might be required, even though more porosity means lower strength. Another example is granular armors, where lower porosity of the armor before molding would mean higher viscosity, making the finished armor more difficult to fabricate but also stronger. With respect to solid propellants, the thrust of a rocket depends roughly on the square of the density (density in composites is proportional to one minus porosity) of the composite propellant.
In general, what is needed is the ability to effectively predict, design and control the structures of granular composites to provide a large degree of control over composite physical characteristics. In particular, what is needed is a way to reduce the porosity of composites in order to improve physical characteristics, and, in many cases, to reduce porosity while maintaining low enough viscosity to retain the ability to be used in fabrication processes.